Crystal structure
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The document discusses various topics related to crystals, including: - Crystals have a periodic arrangement of atoms and can have regular shapes categorized by symmetry. Pharmaceutical crystals often have irregular dendritic shapes. - There are seven crystal systems categorized by symmetry elements like axes and planes. The main systems discussed are cubic, tetragonal, orthorhombic, monoclinic, triclinic, rhombohedral, and hexagonal. - Unit cells are the smallest repeating units that make up the overall crystal structure. They can be primitive, containing one lattice point, or non-primitive with multiple points.
Crystal structure
- 2. A Crystal is a three-dimensional solid which consists of a periodic arrangement of atoms. A crystal is a solid form of substance (ice) Some crystals are very regularly shaped and can be classified into one of several shape categories such rhombic, cubic, hexagonal, tetragonal, orthorhombic, etc. With pharmaceuticals, crystals normally have very irregular shapes due to dendritic growth which is a spiky type appearance like a snowflake. It can be difficult to characterise the size of such a crystal. Crystals are grown to a particular size that is of optimum use to the manufacturer. Typical sizes in pharmaceutical industry are of the order of 50µm. What is Crystal
- 3. Classification of Solids Crystalline materials Non-crystalline materials Glass Rubber and Plastics Poly-crystal (It has an aggregate of many small crystals that are separated by well-defined boundaries) Single crystal (The entire solid consists of only one crystal) Example Non-metallic crystals Metallic crystals Germanium Silicon crystalline carbon etc., Iron Copper Silver Aluminium Tungsten etc.,
- 4. Crystal SymmetryCrystal Symmetry Crystals have inherent symmetry The definite ordered arrangement of the faces and edges of a crystal is known as `crystal symmetry’. It is a powerful tool for the study of the internal structure of crystals. Crystals possess different symmetries or symmetry elements. The seven crystal systems are characterized by three symmetry elements. They are Centre of symmetry Planes of symmetry Axes of symmetry.
- 5. CeCentrentre of Symmetryof Symmetry It is a point such that any line drawn through it will meet the surface of the crystal at equal distances on either side. Since centre lies at equal distances from various symmetrical positions it is also known as `centre of inversions’. It is equivalent to reflection through a point. A Crystal may possess a number of planes or axes of symmetry but it can have only one centre of symmetry. For an unit cell of cubic lattice, the point at the body centre represents’ the `centre of symmetry’ and it is shown in the figure.
- 6. PlaPlanene of Symmetryof Symmetry A crystal is said to have a plane of symmetry, when it is divided by an imaginary plane into two halves, such that one is the mirror image of the other. In the case of a cube, there are three planes of symmetry parallel to the faces of the cube and six diagonal planes of symmetry .
- 7. Axis of SymmetryAxis of Symmetry This is an axis passing through the crystal such that if the crystal is rotated around it through some angle, the crystal remains invariant. The axis is called `n-fold, axis’. If equivalent configuration occurs after rotation of 180º, 120º and 90º, the axes of rotation are known as two-fold, three-fold and four-fold axes of symmetry respectively. If equivalent configuration occurs after rotation of 180º, 120º and 90º, the axes of rotation are known as two-fold, three-fold and four-fold axes of symmetry. If a cube is rotated through 90º, about an axis normal to one of its faces at its mid point, it brings the cube into self coincident position. Hence during one complete rotation about this axis, i.e., through 360º, at four positions the cube is coincident with its original position. Such an axis is called four-fold axes of symmetry or tetrad axis.
- 8. Axis of SymmetryAxis of Symmetry If n=1, the crystal has to be rotated through an angle = 360º, about an axis to achieve self coincidence. Such an axis is called an `identity axis’. Each crystal possesses an infinite number of such axes. If n=2, the crystal has to be rotated through an angle = 180º about an axis to achieve self coincidence. Such an axis is called a `diad axis’. Since there are 12 such edges in a cube, the number of diad axes is six. If n=3, the crystal has to be rotated through an angle = 120º about an axis to achieve self coincidence. Such an axis is called is `triad axis’. In a cube, the axis passing through a solid diagonal acts as a triad axis. Since there are 4 solid diagonals in a cube, the number of triad axis is four.
- 9. Axis of SymmetryAxis of Symmetry If n=4, for every 90º rotation, coincidence is achieved and the axis is termed `tetrad axis’. It is discussed already that a cube has `three’ tetrad axes. If n=6, the corresponding angle of rotation is 60º and the axis of rotation is called a hexad axis. A cubic crystal does not possess any hexad axis. Crystalline solids do not show 5-fold axis of symmetry or any other symmetry axis higher than `six’, Identical repetition of an unit can take place only when we consider 1,2,3,4 and 6 fold axes.
- 10. Symmetrical ElemeSymmetrical Elements of cubents of cube (a) Centre of symmetry 1 (b) Planes of symmetry 9 (Straight planes - 3, Diagonal planes - 6) (c) Diad axes 6 (d) Triad axes 4 (e) Tetrad axes 3 ---- Total number of symmetry elements = 23 ---- Thus the total number of symmetry elements of a cubic structure is 23.
- 11. Lattice is as an array of points in space in which the environment about each point is the same i.e., every point has identical surroundings to that of every other point in the array. Lattice or Space lattice The crystal structure is obtained by adding a unit assembly of atoms to each lattice point. This unit assembly is called basis. A basis may be a single atom or assembly of atoms which is identical in composition, arrangement and orientation. Space lattice + Basis Crystal structure Example • Aluminium and Barium •Sodium chloride NaCl • Potassium chloride KCl Basis
- 12. The unit cell is defined as the smallest geometric figure which is repeated to drive the actual crystal structure Unit cell Primitive cell A primitive cell is the simplest type of unit cell which contains only one lattice point per unit cell (contains lattice points at its corner only) Example: SC – Simple cubic Non-primitive cell If there are more than one lattice point in an unit cell, it is called a non-primitive cell (contains more than one lattice point per unit cell) Example: BCC and FCC
- 14. Cubic (3) Simple, Body-centred, Face-centred Tetragonal (2) Simple, Body-centred, Orthorhombic (4) Simple, Body-centred, Face-centred, Base-centred Monoclinic (2) Simple, Base-centred Triclinic (1) Simple Rhombohedral (1) Simple Hexagonal (1) Simple Types of Crystal systemsTypes of Crystal systems
- 15. Cubic crystal systemCubic crystal system In this crystal system, all the three axial lengths of the unit cell are equal and they are perpendicular to each other a = b = c and α = β = γ = 90o Example: Iron, copper, Sodium Chloride (NaCl), Calcium Fluoride (CaF2) a a a 90o 90o 90o Cubic crystal system Y X Z
- 16. Simple Cubic Body-centred Cubic Face-centred Cubic
- 17. TetragoTetragonal crystal systemcrystal system In this crystal system, two axial lengths of the unit cell are equal and third axial length is either longer or shorter. All the three axes are perpendicular to each other. a = b ≠ c and α = β = γ = 90o Example: Ordinary white tin, Indium. Tetragonal crystal system 90o 90o 90o b a c Y X Z
- 19. Orthorhombic crystal systemOrthorhombic crystal system In this system, three axial lengths of the unit cell are not equal but they are perpendicular to each other a ≠ b ≠ c and α = β = γ = 90o Example: Sulphur, Topaz a b c 90o 90o 90o Orthorhombic crystal system Y X Z
- 20. Simple Body-centred Face-centred Base-centred
- 21. MoMonoclinic crystal systemcrystal system In this system, three axial lengths of the unit cell are not equal. Two axes are perpendicular to each other and third axis is obliquely inclined. a ≠ b ≠ c and α = β = 90o , γ ≠ 90o Example: Sodium sulphite (Na2SO3), Ferrous sulphate (FeSO4). a b c α ꞊ 90 o β 90꞊ o γ ≠ 90o Monoclinic crystal system Y X Z
- 23. TriTriclinic crystal systemcrystal system In this system, three axial lengths of the unit cell are not equal and all the three axes are inclined obliquely to each other. a ≠ b ≠ c and α ≠ β ≠ γ ≠ 90o Example: Copper sulphate (CuSO4), Potassium dichromate (K2Cr2O7). a b c α β γ Triclinic crystal system Y X Z
- 24. RhombohedralRhombohedral crystal systemcrystal system In this system, three axial lengths of the unit cell are equal. They are equally inclined to each other at an angle other than 90o . a = b = c and α = β = γ ≠ 90o Example: Calcite. a a a α β γ Rhombohedral crystal system Y X Z
- 25. HexagoHexagonal crystal systemcrystal system In this crystal system, two axial lengths of the unit cell (horizontal) are equal and lying in one plane at angle 120o with each other The third axial length (vertical) is either longer or shorter than other two and it is perpendicular to this plane. a = b ≠ c and α = β = 90o γ = 120o Example: Quartz, Tourmaline b c a 90o 120o 90o Hexagonal crystal system 120o
- 26. Crystal plaCrystal planeses Miller introduced a set of three numbers to designate a plane in a crystal. This set of three numbers is called Miller indices of the concerned plane. A B C Y X Z 2 2 1